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Chapter 16: Problem 20

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\) b. \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\) c. \(\mathrm{BaF}_{2}\)

Short Answer

Expert verified
The balanced equations for the dissolution reactions and solubility product expressions for the given solids are as follows: a. \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\): \[ \mathrm{Ag}_{2} \mathrm{CO}_{3} \rightleftharpoons 2\mathrm{Ag^{+}} + \mathrm{CO}_{3}^{2-}\] \[ K_{sp} = [\mathrm{Ag^{+}}]^{2}[\mathrm{CO}_{3}^{2-}] \] b. \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\): \[ \mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3} \rightleftharpoons \mathrm{Ce}^{3+} + 3\mathrm{IO}_{3}^{-}\] \[ K_{sp} = [\mathrm{Ce}^{3+}][\mathrm{IO}_{3}^{-}]^{3} \] c. \(\mathrm{BaF}_{2}\): \[ \mathrm{BaF}_{2} \rightleftharpoons \mathrm{Ba}^{2+} + 2\mathrm{F}^{-}\] \[ K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^{2} \]

Step by step solution

01

Write the balanced equations

We will break down each solid into its constituent ions during dissolution: a. For \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\), we have: \[ \mathrm{Ag}_{2} \mathrm{CO}_{3} \rightleftharpoons 2\mathrm{Ag^{+}} + \mathrm{CO}_{3}^{2-}\] b. For \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\), we have: \[ \mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3} \rightleftharpoons \mathrm{Ce}^{3+} + 3\mathrm{IO}_{3}^{-}\] c. For \(\mathrm{BaF}_{2}\), we have: \[ \mathrm{BaF}_{2} \rightleftharpoons \mathrm{Ba}^{2+} + 2\mathrm{F}^{-}\]
02

Find solubility product expressions

Now, we can find the solubility product expressions by multiplying the concentrations of the resulting ions, raised to the power of their stoichiometric coefficients in the balanced equation. a. For \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\): \[ K_{sp} = [\mathrm{Ag^{+}}]^{2}[\mathrm{CO}_{3}^{2-}] \] b. For \(\mathrm{Ce}\left(\mathrm{IO}_{3}\right)_{3}\): \[ K_{sp} = [\mathrm{Ce}^{3+}][\mathrm{IO}_{3}^{-}]^{3} \] c. For \(\mathrm{BaF}_{2}\): \[ K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{F}^{-}]^{2} \] These are the solubility product expressions for the given solids.

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Most popular questions from this chapter

Devise as many ways as you can to experimentally determine the \(K_{\mathrm{sp}}\) value of a solid. Explain why each of these would work.

When \(\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) is added to a solution containing a metal ion and a precipitate forms, the precipitate generally could be one of two possibilities. What are the two possibilities?

a. Calculate the molar solubility of AgBr in pure water. \(K_{\text {sp }}\) for \(\mathrm{AgBr}\) is \(5.0 \times 10^{-13}\) b. Calculate the molar solubility of \(\mathrm{AgBr}\) in \(3.0 \mathrm{M} \mathrm{NH}_{3}\). The overall formation constant for \(\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}{ }^{+}\) is \(1.7 \times 10^{7}\), that is. \(\mathrm{Ag}^{+}(a q)+2 \mathrm{NH}_{3}(a q) \longrightarrow \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q) \quad K=1.7 \times 10^{7}\) c. Compare the calculated solubilities from parts a and b. Explain any differences. d. What mass of AgBr will dissolve in \(250.0 \mathrm{~mL}\) of \(3.0 \mathrm{M}\) \(\mathrm{NH}_{3} ?\) e. What effect does adding \(\mathrm{HNO}_{3}\) have on the solubilities calculated in parts a and b?

Calculate the concentration of \(\mathrm{Pb}^{2+}\) in each of the following. a. a saturated solution of \(\mathrm{Pb}(\mathrm{OH})_{2}, K_{\mathrm{sp}}=1.2 \times 10^{-15}\) b. a saturated solution of \(\mathrm{Pb}(\mathrm{OH})_{2}\) buffered at \(\mathrm{pH}=13.00\) c. Ethylenediaminetetraacetate \(\left(\mathrm{EDTA}^{4-}\right)\) is used as a complexing agent in chemical analysis and has the following structure: Solutions of EDTA \(^{4-}\) are used to treat heavy metal poisoning by removing the heavy metal in the form of a soluble complex ion. The reaction of EDTA \(^{4-}\) with \(\mathrm{Pb}^{2+}\) is \(\begin{aligned} \mathrm{Pb}^{2+}(a q)+\mathrm{EDTA}^{4-}(a q) \rightleftharpoons \mathrm{PbEDTA}^{2-}(a q) & \\ K &=1.1 \times 10^{18} \end{aligned}\) Consider a solution with \(0.010\) mole of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) added to 1.0 L of an aqueous solution buffered at \(\mathrm{pH}=13.00\) and containing \(0.050 M\) NasEDTA. Does \(\mathrm{Pb}(\mathrm{OH})_{2}\) precipitate from this solution?

Consider a solution made by mixing \(500.0 \mathrm{~mL}\) of \(4.0 \mathrm{M} \mathrm{NH}_{3}\) and \(500.0 \mathrm{~mL}\) of \(0.40 \mathrm{M} \mathrm{AgNO}_{3} \cdot \mathrm{Ag}^{+}\) reacts with \(\mathrm{NH}_{3}\) to form \(\begin{aligned} \mathrm{AgNH}_{3}{ }^{+} \text {and } \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}+: \\ \mathrm{Ag}^{+}(a q)+\mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{AgNH}_{3}{ }^{+}(a q) & K_{1}=2.1 \times 10^{3} \\ \mathrm{AgNH}_{3}^{+}(a q)+\mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}^{+}(a q) & K_{2}=8.2 \times 10^{3} \end{aligned}\) Determine the concentration of all species in solution.
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